The text consists of two subject matters, viz., Matrix Analysis of Structures and the Theory of Structural Stability, its principles and applications. Advent of computer paved way for the discovery of two novel methods, namely, Matrix Analysis and Finite Element Method. Because of these two methods, the conventional Slope Deflection, Moment Distribution, Column Analogy, Elastic Center, Kani's Method, Naylor's method, etc., will either go into desuetude or will be taught to a limited extent in the curriculum. In this text, the Matrix Analysis is dealt within an exhaustive manner serving as a prelude to comprehend and appreciate the more powerful FEM in the postgraduate course. Almost all structures include in them compression elements. In beams, part of the section is under compression. When the components are slender and thin, they have a tendency for buckling due to compression.In this text many novel formulations have been included to determine the critical loads of non-prismatic columns, square, rectangular and circular plates, elastic frames, rings, etc. These approximate theories are simple in concept, easy to work with and efficacious. Because of this fact, old and rigorous approximate procedures will be dispensed with in future. The subject matter advanced in this text may provide an effective background to develop new theories related to neural networks, genetic algorithm, biomechanics,